I have a 2013 or 14 specialized hardrock disk 29er. I wanted to replace the crank, looking at these two:

https://www.niagaracycle.com/categor...0-square-black

https://www.niagaracycle.com/categor...re-taper-black

The existing crank is Suntour, so will these work? I wasn't sure about the 113 vs 122mm spindle length. I'm having a hard time finding info on the exact specs of my bike. It's the one pictured here:

Livin' in Paradise: New Ride - Specialized Hardrock Disc 29

Anything I can measure on my bike to tell?

Why limit yourself to square taper. If they are what you want that is fine. All you need to know is the size of your BB Shell and whether it's a press fit or threaded. A call to a bike shop that sells Specialized should get you the exact size and info pretty quick if no one here that knows for certain sees your post.

The length of your bb shell on the frame measured from left side to right in millimeters is one thing that helps. It can be hard to measure accurately on some bikes if the BB is installed. But a mm makes a difference for some type cranks and BB's so calipers are helpful.

You also need to know the inside diameter. Millimeters again if it is press fit. But threaded BB's might be inches too. A common threaded is 1.37in.x24 tpi. If there is any writing on your current BB, that might indicate its size. Got a pic?

If you like square tapers, that's fine. But there is a world of other cranks out there if you are willing to spend an extra 20 bucks for a new bb.

Cartridge BBs have to match the crank as well as the bike. It appears your bike is BSA threaded so you just need to know the width of the frame - either 68 or 73, easily measured with a ruler. That width plus the width needed for the crank determine the cartridge BB to purchase.
You can either pull the BB out of your bike to see what it is and if it will work or order a new one in the recommended width with the crank you are looking at.
You should look at a modern crank like a Deore or similar.

Latest cranks have external bearings, and fix the drive arm and a tube spindle in a single piece,

that you pass through the bearing assemblies, then put the left crank arm on.

it removes variations in length, you just buy one for your MTB.